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Search: id:A111661
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| A111661 |
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Expansion of eta(q)^4*eta(q^2)*eta(q^6)^5/eta(q^3)^4 in powers of q. |
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+0
1
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| 1, -4, 1, 16, -24, -4, 50, -64, 1, 96, -120, 16, 170, -200, -24, 256, -288, -4, 362, -384, 50, 480, -528, -64, 601, -680, 1, 800, -840, 96, 962, -1024, -120, 1152, -1200, 16, 1370, -1448, 170, 1536, -1680, -200, 1850, -1920, -24, 2112, -2208, 256, 2451, -2404, -288, 2720, -2808, -4
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 226 Entry 4(i).
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FORMULA
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Euler transform of period 6 sequence [ -4, -5, 0, -5, -4, -6, ...].
G.f.: Sum_{k>0} kronecker(k, 3)*k^2*x^k/(1-x^(2k)) = x Product_{k>0} (1-x^k)^4*(1-x^(2k))*(1+x^(3k))^5*(1-x^(3k)).
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (n/d%2)*d^2*kronecker(d, 3)))
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)^4*eta(x^2+A)*eta(x^6+A)^5/eta(x^3+A)^4, n))}
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CROSSREFS
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Sequence in context: A099394 A059991 A002568 this_sequence A072651 A093035 A126791
Adjacent sequences: A111658 A111659 A111660 this_sequence A111662 A111663 A111664
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Aug 08 2005
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